Chapter  R GEOSTATISTICS


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1 Chapter  R GEOSTATISTICS
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15 23 rd Feasibility Study of a Mining Project under Uncertainty: Can the Real Options Approach be a Viable Solution? M. H. Basiri 1, A. A. Khodayari 2, A. Saeedi 1, F. Javadnejad 1 1 Department of Mining Engineering, Tarbiat Modares University, Tehran, Iran 2 Department of Mining Engineering, Tehran University, Tehran, Iran ABSTRACT Nowadays, making investment decision in the mine sectors is faced with huge challenge of uncertainties particularly when this investing is highly capital intensive and long term. These uncertainties are originated from environmental, market and political changes. In such condition mining companies cannot have a stable vision of their enterprises. Therefore, they should consider the investments which encompass flexibility by adapting market conditions. Traditional discounted cash flows (DCF) or net present value (NPV) methods constitute most investment decision making structures. In recent years, the Real Options Approach (ROA) is presented based on the advanced options theory technique of DCF and NPV. In this paper the both techniques are compared and evaluate the role of real options valuation in a mining project (Kahnoj titan plant as a case study) feasibility studies. The management team s flexibility to change the project s course is embedded in the form of options to abandon, expand and contract of the project. Monte Carlo simulationbased method using MATLAB software commandline functions is used for valuation of the options values. Based on the results, the values of the project s abandonment, contraction and expansion options are estimated 18,241,730 and 13,407,795 and 219,909,955 dollars respectively. The added values could be substantial for a noneconomic project and it is close to break point estimated by DCF analysis (with the net present value of 1,695,397 dollars). This research capable to be implemented into the similar projects that needed managerial decisions making using real options. Key words: Feasibility Study, uncertainty, Monte Carlo simulation, real options approach 1 INTRODUCTION Investments in mining projects and related industries are quite different from the other projects. All mining projects are associated with uncertainties in the future profitability. This uncertainty affects on the ore prices, operating cost, and so on. Investment in the mining projects is encountered a delay between decision making steps and investment procedures. A successful investor is the one who has the managerial flexibility and ability to delay, expand, contradict, or abandon the project. There are varieties of factors that assist the investor to have a right investment decision making. Valuation of the mining project is depending on the different factors such as the world ore prices, operating costs, and so on. DCF techniques are commonly used for economic evaluation of mining projects. However these techniques, due to the lack of consideration of the managerial flexibility, may underestimate some projects. In this paper, the real options theory is applied to meet theses flexibilities. 2 LITERATURE REVIEW ROA has considered recently among some researchers and economists. They have 1727
16 M. H. Basiri, A. A. Khodayari, A. Saeedi, F. Javadnejad mentionedroa as means of betterassessing projects under uncertainty. Under uncertainty conditions, the ROA presents a better result comparison with the traditional DCF analyses such as NPV and the internal rate of return (IRR) methods. ROA is capable to embed the value of managerial flexibility to change or revise the project course based on the new market conditions. Therefore, using the same discounting rate, the value of a project calculated by the ROA is always higher than that valuated by the traditional NPV method. Moyen et al. and Miller and Park explained uncertainty and profitability of the project as the cause of discrepancy between the ROA and the DCF estimates (Moyen et al., (1996)), (Miller et al., 2002). The first and likely most enforceable model for assessing options isblack and Scholesmodel (Black, 1973). However, as explained by Berridge and Schumacher (2004), the Black Scholes model is just applicable for valuing European options not for American options (Berridge, 2002). The lattice method presented is another common technique for valuingoptions (Cox et al., 1979). Barraquand and Martineau (1995) criticized the application of lattice method by offering limitations of which. They mentioned that the method becomes inapplicable when projects facing multiple uncertainty. (Barraquand et al., 1995) developed the finite difference method for options valuation, however this method have the same liabilities as the lattice method (Brennan et al., 1978). The first time proposed by Boyle the Monte Carlo method based on simulation is used for valuing European options (Bpyle 1977). Afterward an improvedversion of the Monte Carlo method wasdeveloped to value American options. Despite the previous techniques, the simulationbased techniques have better performance facing multiple uncertainties. This means that both product volatility over time and cashflows variability can be embedded in the valuation (Longstaff et al., 2001). The ROA is not a new technique for natural resource investment applications. Since the first paper applying the ROA to value a simple copper mine was published by Brennan and Schwartz, considerable work has beendone employing the same concepts of uncertainty and operating flexibility. (Brennan et al., 1985) applied the ROA to value management flexibility to develop petroleum leases (Paddock et al., 1988). Trigeorgis addressed the consequence of embedding the distinct real options on the value of a natural resource extractionproject (Trigeorgis, 1993). Using data from Canadian copper mines illustrated an analogy between the NPV method and the option valuation method. This comparison shows that the NPV method underestimates mining projects (Moyen et al., 1996). McCarthy and Monkhouse offered a trinomial latticemethod for valuing a copper mine have both wait and abandon options (McCarthy, 2003). Abdel Sabour and Poulin (2006) and Roussos G. Dimitrakopoulos, Sabry A. Abdel Sabour (2007) are other significant researchers who conducted assessing mine plans under uncertainty(sabour et la., 2007). Graham A. Davis and Alexandra M. Newman presented a Modern Strategic Mine Planning using ROA technique (Graham et al., 2008). S Shafiee1, E Topal and M Nehring used an adjusted Real Option Valuation to maximize mining project value using Century Mine case study (Shafiee et al., 2009). Luis Martinez using real options presented a project valuation for open pit mining risks and merged econometric techniques (Martinez, 2011). 3 TRADITIONAL EVALUATION METHOD DCF and the associated NPV techniques have traditionally provided the major tools for project evaluation. The discounted cash flow formula, equation (1), is derived from the future value formula for calculating the time value of money and compounding returns. (1) 1728
17 23 rd Where NPV is the net present value, C 0 to C T are the cash flows expected through the project s life (T) and r is discounting riskadjusted rate. NPV analysis evaluates the cash flows forecasted to be delivered by a project by discounting them back to the present using the time span of the project and the firm's weighted average cost of capital. If the result is positive, then the firm should invest in the project. If negative, the firm should not invest in the project. In addition Internal Rate of Return (IRR) cloud be calculated by giving the equation equal zero. DCF is used by analysts to evaluate projects. However, this tool has certain limitations. For example, if the project's cash flows and decisions are likely faced to many uncertainties (where managers have the flexibility to change the course of the project), part of the value related to these options could be not incorporated in the valuationprocess. 4 REAL OPTION APPROACH Nowadays management is looking for a way to reduce uncertainty and to assess the impact of managerial uncertainty on project. ROA has been developed to promote this goal. This approach has provided a basis for the development in financial and decision making analyses. ROA is one of the modern valuation methods that provide a tool to adapt and revise mining projects under uncertainty and future variable movements. A lot of progresses that have been done in the Real Option literature have changed the way of thinking about an investment opportunity. During project management, managers may do several choices about project characteristics every time new information from market is available. ROA is the way to respond to market changes. This possibility thatmanagers have to adapt their decisions to the change of market has value that must be considered during the decision making process. Therefore, this flexibility creates options that increase the value of the project and determines the failure of the traditional technique (such as NPV). ROA accounts for a range of possible outcomes over the life of a project using stochastic processes and calculates a composite options value for a project, considering only those outcomes that are favorable (i.e., options are exercised) and ignoring those that are not (letting the options expire). This assumes that the decision makers will always take the valuemaximizing decision at each decision point in the project life cycle. Whereas DCF accounts for the downside of a project by using a riskadjusted discount rate, ROA captures the value of the project for its upside potential by accounting for proper managerial decisions that would presumably be taken to limit the downside risk. Table 1 summarizes the major differences between DCF and ROA. 4.1 Options As discussed if there is large uncertainty related to the project cash flows and contingent decisions are involved, where mangers have flexibility to change the course of the project, ROA can be applied for project valuation using different options. In this research several real options embedded virtually in every project are investigated and used to calculate the generated additional value of managerial flexibility. Following options are the focus of this paper: Option to expand Option to contract Option to wait Option to abandon For every mentioned options, this research focuses on one or two aspects (such as practical issues, input parameter variability, etc.) that are most relevant to that option type. For example, the option to expand issue involves how the option size influences the option value. Using the option to contract of the scale, the impact of the volatility factor on the option value is highlighted. 1729
18 M. H. Basiri, A. A. Khodayari, A. Saeedi, F. Javadnejad Table 1: the major differences between DCF and ROA Real Options Analysis Discounted Cash Flow Recognizes the value in managerial flexibility to alter the course of a project Uncertainty is a key factor that drives the option s value. The longterm strategic value of the project is considered because of the flexibility with decision making. Payoff itself is adjusted for risk and then discounted at a riskfree rate. Risk is expressed in the probability distribution of the payoff. All or nothing strategy. Does not capture the value of managerial flexibility during the project life cycle. Uncertainty with future project outcomes not considered. Undervalues the asset that currently (or in the near term) produces little or no cash flow. Expected payoff is discounted at a rate adjusted for risk. Risk is expressed as a discount premium. Investment cost is discounted at the same rate as the payoff, that is, at a riskfree rate. The analysis of the option to wait discusses how leakage of asset value can be accounted for in the options calculations. And finally, in the case of the option to abandon how to solve the options problem for various strike prices is illustrated. Indeed How to calculate the probability of exercising the option of abandoning the project is presented Option to expand Option to expand is usual in any project. In some cases, the initial NPV can be marginal or even negative, but when growth opportunities with high uncertainty exist, the option to expand can provide a considerable value. Without regarding to an expansion option, great opportunities may be overlooked. Investment for expansion is the strike price that will be acquired as a result of exercising the option. The option would be activated if the expected payoff is greater than the strike price Option to contract Once a project has been developed, management may have the option to decelerate the production rate or change the scale of production. In a project, there might Investment cost is typically discounted at the same rate as the payoff, that is, at a riskadjusted rate. be the option to decrease production by contemplating scaling down its operations by either selling or outsourcing one or more plants to gain efficiencies through stabilization. The option to contract is significant in today s competitive marketplace, where companies need to downsize or outsource swiftly as external conditions change. Organizations can hedge themselves through strategically created options to contract. The option to contract has the same characteristics as a put option, because the option value increases as the value of the underlying asset decreases Option to wait Investing in a mining project has much in common with exercising a financial option. First, both are at least partially irreversible. Second, timing is crucial. Indeed, taking an irreversible action means forfeiting the option to wait for new information concerning market conditions. (Margaret E. Slade, 2000). Option to defer investment, an opportunity to invest at some point in the future, may be more valuable than an opportunity to invest immediately. A deferral option gives an investor the chance to wait until conditions become more favorable, or to abandon a project if 1730
19 23 rd conditions deteriorate. Such options allow a firm to delay an investment until it's sure about other relevant issues Option to abandon Management may decide to abandon the project and sell any accumulated capital equipment in the open market. Alternatively, it may sell the project, or its share in the project, to another company whose strategic plans make the project more attractive. Selling for salvage value would be similar to exercising an American put option. If the value of the project falls below its liquidation value, the company can exercise its put option. To clarify the mechanism of this valuation process, assume that the only operating flexibility available to the mine manager is to close the mine early. This option is irreversible. At any time the decision to abandon the mine is made by comparing the expected value of all future cash flows and the abandonment cost at that time. 5 MONTE CARLO SIMULATION To asses real options value partial differential equations, dynamic programming, and simulation methods can be applied. In this paper referred to Monte Carlo simulation method. The simulation method for solving real options problems is similar to the Monte Carlo technique for DCF analysis. Traditional Monte Carlo simulation has been considered a powerful and flexible tool for capital budgeting for a very long time. It involves simulation of thousands of paths the underlying asset value may take during the option life given the boundaries of uncertainty defined by the volatility of the asset value. 6 PRACTICAL APPLICATION: FEASIBILITY STUDY OF A MINING PROJECT UNDER UNCERTAINTY The final goal of mine managers and decision makers is to make decisions that seem to be the optimum based on the information available at the designing time. In this study, the applicability and usefulness of the simulationbased ROA method is investigated. Proposed method is applied to choose the best mine plan among different feasible options. Thought fiveyear life of options, Iranian Kahnoj Titan is selected to perform the reality examination. Kahnoj Titan faces a myriad of uncertainties and decisionmaking flexibilities. Production of this industry plant consists of titan pigment, titan magnetite concentrate, and sorrel iron. By using the traditional DCF technique this project was evaluated (Table 2). As it shown in the table, the NPV is negative and the IRR is lower than the risk rate. This situation provides a suitable platform to conduct the real options valuation method on this project. Table 2: DCF technique analysis of the project Year Cash Flows Ye Cash Flows ($) ar ($) 37,975, ,425, ,222, ,447, , ,289, ,858, ,280, ,136, ,273, ,501, ,267, ,277, ,261, ,425, ,257, ,425, ,252, ,425, ,249, ,425, ,247, ,425, ,760,454 RiskAdjusted Rate 25% Net Present Value (NPV) 1,695,397 $ Internal Rate of Return (IRR) 22% 7 SOLVING THE PROBLEM USING THE REAL OPTIONS VALUATION MONTE CARLO SIMULATIONBASED First the input parameters required to conduct the simulations are defined: Current value of the underlying asset (So) Strike price (X) Option life (T) Riskfree rate corresponding to the option life (r) 1731
20 M. H. Basiri, A. A. Khodayari, A. Saeedi, F. Javadnejad t) 7.1 Estimation of current value of the asset With the real options, the current value of the underlying asset value is estimated from the cash flows that asset is expected to generate over the project life. In the other hand, the present value of the expected free cash flows based on the DCF calculation is regarded the value of the underlying asset. First, the future revenues are calculated based on the number of units expected to be sold, price per unit, operation cost, and then it discounted to the present time by an appropriate risk adjusted discount rate. 7.2 Calculating volatility factor Volatility refers to the variability of the asset value and as an important input variable; it can have a significant impact on the option options models. It is the volatility of the product prices, which have a significant impact on the cash flow returns. In this reach the volatility factor for each product is measured as the standard deviation of the natural logarithm of product prices. And then according to the weighted proportion of each product in cash flows returns, the volatility factor is calculated. 7.3 Exercise or strike price In the real options world, exercising an option typically involves development of a product, construction of a new facility, launching a large marketing campaign, etc., which does not happen in an instant but in fact takes a long time. The strike price or the investment cost directly impacts the option value. Dealing with expansion or contraction options in this research Approximate costs for exercising the options can be obtained through the rule of sixtenths (equation 2). As shown in table, the cost of a similar item of different size or capacity (double or half capacity) for mentioned options is developed. (2) Where C B is the approximate cost ($) of equipment having size S B (cfm, Hp, ft 2, or whatever), C A is the known cost ($) of equipment having corresponding size S A (same units as S B ), S B /S A is known as the size factor (dimensionless). In relation to the abandon option if the project payoff is not attractive, the option to abandon the project is executable. Exercising the project abandon could minimize the losses by either selling off the project s salable equipment or reducing production costs. This option has the characteristics of a put option. The strike prices of these options are presented in Table Simulation In this study, The Monte Carlo simulation is used to simulate the thousands paths of the uncertain asset values, defined by equation (3) through randomly and changing values. To simulating every time increment asset value, the underlying asset value is again calculated for the next time increment using the same equation. In this fashion, asset values for each time step are calculated until the end of the option life. Finally, by applying the decision rule, maximization of the value, the value at the end of the fifth year is compared with strike price of each option. If this value was more than the cost of exercising the option, the option value for that simulation would be the difference between the asset value and its strike price. Otherwise, that option would be worthless and thus, zero value is allocated for it. The Option values for each simulation are discounted to their current values using a riskfree rate and ultimately the mean of which is considered the real option value. Input parameters at table (5) are determined for each real world option. The asset value, whichmay has fluctuations over the option life, is defined by the following equation. 1732
21 23 rd St = S t1 +S t1 ) (3) Where S t and S t 1 are the underlying asset values at time t and time t is the volatility of the underlying asset value; normal distribution with mean of zero and a variance of 1. In this research a commandbased MATLAB simulation was conducted using the volatility factor. A Path is created for each simulated underlying asset value over the option life. Running 100,000 trials develops millions simulated value paths. The average of the option values from such numbers of trials in the case study is the value of the option at the end of five years. Table 6 shows the results of the simulation using the first 20 trials as a sample. The probability of exercising the options, expansion, contraction and abandonment of the project, are 0.32%, 78.02%, 99.97% of the time respectively. And the estimated average values for each mentioned option are 13,407, 221,605,352 and 19,937,127dollars respectively. The added values could be substantial for a noneconomic project close to break point estimated by DCF analysis (whit the net present value of 1,695,397 dollars). 8 CONCLUSION This paper proposed an approach to investigate the role of the real options valuation in a particular mine, Titan Kahnoj plant. Using the ROA provides incorporating managerial flexibility to make investment decisions. To examine the performances of the ROA versus the traditional NPV method and its advantage, a commandbased Monte Carlo simulation thought MATLAB software was carried out. Both methods were applied for valuation of the case study. The managerial flexibility to change the project course was considered in the form of the main options (expansion, contraction and abandonment options). This research can be suitable to discuss of the implementation and management decisions using real options to go out from the current situation in similar projects. REFERENCES Abdel Sabour, S.A., Poulin, R., Valuing real capital investments using the leastsquares Monte Carlo method. Eng. Econom. 51 (2), Barraquand, J., Numerical valuation of high dimensional multivariate European securities. Manage. Sci. 41 (12), Berridge, S., Schumacher, J.M., An irregular grid method for high dimensional freeboundary problems in finance. Future Gener. Comput. Syst. 20, Black, F., Scholes, M., The pricing of options and corporate liabilities. J. Political Econom. 81 (3), Boyle, P., Options: a Monte Carlo approach. J. Financial Econom. 4 (3), Brennan, M.J., Schwartz, E.S., The valuation of American put options. J. Finance 32 (2), Brennan, M.J., Schwartz, E.S., Finite difference methods and jump processes arising in the pricing of contingent claims: a synthesis. J. Financial Quant. Anal. 13, Brennan, M.J., Schwartz, E.S., Evaluating natural resource investments. J. Bus. 58 (2), Broadie, M., Glasserman, P., Pricing Americanstyle securities using simulation. J. Econom. Dyn. Control 21, Cox, J.C., ROAs, S.A., Rubinstein, M., Option pricing: a simplified approach. J. Financial Econom. 7 (3), Dixit, A.K., Pindyck, R.S., Investment under uncertainty. Princeton University Press, New Jersey. Kamrad, B., Ernst, R., An economic model for evaluating mining and manufacturing ventures with output yield uncertainty. Oper. Res. 49 (5), Kelly, S., A binomial lattice approach for valuing a mining property IPO. Quart. Rev. Econom. Finance 38, Kodukula, P., Papudesu Ch., Project Guide. J.ROAs Publishing. Longstaff, F.A., Schwartz, E.S., Valuing American options by simulation: a simple leastsquares approach. Rev. Financial Stud. 14 (1),
22 M. H. Basiri, A. A. Khodayari, A. Saeedi, F. Javadnejad Mardones, J.L., Option valuation of real assets: application to a copper mine with operating flexibility. Resour. Policy 19 (1), Miller, L.T., Park, C.S., Decision making under uncertaintyreal options to the rescue? Eng. Econom. 47 (2), Moel, A., Tufano, P., When are real options exercised? An empirical study of mine closings. Rev. Financial Stud. 15 (1), Moel, A., Tufano, P., When are real options exercised? An empirical study of mine closings. Rev. Financial Stud. 15 (1), Moyen, N., Slade, M., Uppal, R., Valuing risk and flexibility: a comparison of methods. Resour. Policy 22 (1/2), Paddock, J.L., Siegel, D.R., Smith, J.L., Option valuation of claims on real assets: the case of offshore petroleum leases. Quart. J. Econom. 103 (3), Samis, M., Davis, G.A., Laughton, D., Poulin, R., Valuing uncertain asset cash flows when there are no options: a real options approach. Resour. Policy 30, Samis, M., Poulin, R., Valuing management flexibility: a basis to compare the standard DCF and MAP frameworks. CIM Bull. 91 (1019), Schwartz, E.S., The stochastic behavior of commodity prices: implications for valuation and hedging. J. Finance 52 (3), Slade, M.E., Valuing managerial flexibility: an application of real option theory to mining investments. J. Environ. Econom. Manage. 41, Trigeorgis, L., The nature of option interactions and the valuation of investments with multiple real options. J. Financial Quant. Anal. 28 (1), Trigeorgis, L., Real Options: Managerial Flexibility and Strategy in Resource Allocation. MIT Press, Cambridge, MA. Tufano, P., Moel, A., Bidding for Antamina: incentives in a real option context. In: Brennan, M.J., Trigeorgis, L. (Eds.), Project Flexibility, Agency and Competition. Oxford University Press, Oxford, pp APPENDIX Table 3: Calculation of the proportion of each product in cash flow returns and asset value. Year Income of Sorel Iron ($) Income of Titan Pigment ($) Income of Titan magnetite concentrate ($) Operational Cost ($) Cash flows ($) 0 14,400,000 21,000,000 1,130,000 2,481, ,048, ,880,000 42,000,000 2,260,000 3,481, ,177, ,240,000 47,250,000 2,542,500 4,962, ,449, ,600,000 52,500,000 2,825,000 5,582, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721, ,600,000 52,500,000 2,825,000 6,203, ,721,763 Asset value (S 0 ) 179,764,
23 23 rd Table 4: calculation of the volatility factor. Year P t ($/ton) Ratio(P t /P t1 ) ln Ratio Deviation Deviation^2 Volatilit y Titan Magnetite Concentrate (T.M.C.) Mean Titan Pigment (T.P.) Mean Sorrel Iron (S.I.) Mean The exercised volatility % 1735
24 M. H. Basiri, A. A. Khodayari, A. Saeedi, F. Javadnejad Table 5: Monte Carlo simulation input parameters and results. Table 6: The First 20 Simulation Trials for abandonment option
25 23 rd A Fuzzy VIKOR Technique to Selection of Optimum Underground Mining Method for Jajarm Bauxite Mine, Iran A. Jalili, K. Shahriar, A. Sadri Department of Mining and Metallurgical Engineering, Amirkabir University of Technology (Tehran PolyTechnic), Tehran, Iran ABSTRACT Underground mining method (UMM) selection is the first and one of the most crucial decisions that should be made by mining engineers. In this regard some of the parameters such as geological and geotechnical properties, economic parameters and geographical factors are involved. Choosing a suitable underground mining method to extract mineral deposits is very important in terms of the economics, safety and the productivity of mining operations. This paper attempts to demonstrate the calculation of the weighting factors for each selected underground mining method. In practice, underground mining method could be selected using multiple criteria decision making (MCDM) techniqes and decision makers have always some difficulties in making the right decision in the multiple criteria environment. Most multicriteria methods focus on ranking and selecting from a set of alternatives. In this research Jajarm bauxite mine was selected as a case study and optimal method of mining for this mine was proposed using fuzzy VIKOR technique. The the fuzzy VIKOR technique was developed to solve MCDM problems with conflicting and noncommensurable criteria assuming that compromising is acceptable to resolve conflicts. In this technique also importance weights of decision makers opinions have considered different. Finally according to this technique the most appropriate mining methods for this mine were ranked. Keywords: Multicriteria decision making, VIKOR, Fuzzy logic, mining method selection 1 INTRODUCTION Relaible selection of UMM is necessary to optimal design of mine (Alpay & Yavuz, 2009). To make a suitable decision on underground mining method selection, all known criteria related to the problem should be analyzed. Although an increasing in the number of related criteria makes the problem more complicated, this may also increase the correctness of the decision. Due to the arising complexity in the decision process, many conventional methods are able to consider limited criteria and may be generally deficient. Therefore, it is clearly seen that assessing all of the known criteria connected to the mining method selection by combining the decision making process is extremely significant (Hartman & Mutmansky, 2002). Once selected a mining method, it is nearly impossible to change it owing to the rising costs and mining losses, it is very important to reanalyze the decision made before carrying it out (Naghadehi & Ataei, 2009). In this sensitively analysis was generally used on the final decision (Alpay & Yavuz, 2009). The aim of this paper is to compare the many different geological, geotechnical, economical and technical aspects in the selection of the most appropriate underground mining method for Jajarm 1737
26 A. Jalili, K. Shahriar, A. Sadri Bauxite Mine in Iran, with reference to some different extraction methods. The comparison has been performed with the combination of the VIKOR method and fuzzy logic (Fuzzy VIKOR Method). In the multiple criteria decision making (MCDM) problems, since that the valuation of criteria leads to diverse opinions and meanings, each attribute should be imported with a specific importance weight (Chen, Tzeng & Ding, 2003). A question rises up here and that is how this importance weight could be calculated? In literature, most of the typical MCDM methods leave this part to decision makers, while sometimes it would be useful to engage endusers into the decision making process. To obtain a better weighting system, weighting methods are usually divided into two categories: subjective methods and objective methods (Wang & Lee, 2009). While subjective methods determine weights solely based on the preference or judgments of decision makers, objective methods utilize mathematical models, such as entropy method or multiple objective programming, automatically without considering the decision makers preferences. The approach with objective weighting is particularly applicable for situations where reliable subjective weights cannot be obtained (Deng, Yeh & Willis, 2000). On the other hand, new researches entail new MCDM approaches such as VIKOR. VIKOR is a helpful tool in multicriteria decision making (MCDM), the obtained compromise solution could be accepted by the decision makers because it provides a maximum group utility (represented by min S,) of the majority, and a minimum of the individual regret (represented by min R) of the opponent. 2 VIKOR TECHNIQUE Vlsekriterijumska Optimizacija I Kompromisno Resenje (i.e. VIKOR) method was developed by Opricovic in 1998 for multicriteria optimization of complex systems (Opricovic & Tzeng, 2002). VIKOR focuses on ranking and sorting a set of alternatives against various, or possibly conflicting and noncommensurable, decision criteria assuming that compromising is acceptable to resolve conflicts. Similar to TOPSIS as a MCDM method, VIKOR relies on an aggregating function that represents closeness to the ideal, but unlike TOPSIS, introduces the ranking index based on the particular measure of closeness to the ideal solution. This method uses linear normalization to eliminate units of criterion functions (Opricovic & Tzeng, 2004). The VIKOR method was developed for the multicriteria optimization of complex systems. It determines the compromise ranking list and the compromise solution. The weight stability intervals for the preferred stability of the compromise solution can be obtained from the initial weights given by the AHP in the traditional method. This traditional method focuses on ranking and selection from a set of alternatives in cases of conflicting criteria. It introduces a multicriteria ranking index based on the particular measure of closeness to the ideal solution (Chiu & Tzeng, 2012). The VIKOR method began with the form of L p metric, which was used as an aggregating function in a compromise programming method and developed into the multicriteria measure for compromise ranking. We assume the alternatives are denoted as A 1,A 2,...,A i,..., A m. w j is the weight of the jth criterion, expressing the relative importance of the criteria, where j = 1, 2,..., n, and n is the number of criteria. The rating of the jth criterion is denoted by f ij for alternative A i. The form of L p metric is formulated as follows: 1738
27 23 rd 1/ p n p p Li j ( f j fij ) / ( f j f j ) (1) ji 1 p ;i=1,2,,m The VIKOR method is not only generated with the above form of L p metric, but also p 1 uses L p i (as S i in Eq. (2)) and L i (as R i in Eq. (3)) to formulate the ranking measure. (chen et al.,2011; Chiu & Tzeng, 2012). Step 2: Compute the values S i and R i, i = 1, 2,...,m, using the relations Eq.(4)&(5). Step 3: Compute the Q j values for i=1, 2,, m with the relation Eq.(6). n i j j ij j j j1 S ( f f ) / ( f f ) (4) max ( R f f ) / ( f f ) (5) i j j j ij j j n p1 i i j j ij j j j1 L S ( f f ) / ( f f ) (2) p max ( L R f f ) / ( f f ) (3) i i j j j ij j j When p is small, the group utility is emphasized (such as p=1) and as p increases, the individual regrets/gaps receive more weight(chiu & Tzeng,2012). In addition, the p compromise solution min i Li will be chosen because its value is closest to the ideal/aspired level. Therefore, min i S i expresses the minimization of the average sum of the individual regrets/gaps and min i R i expresses the minimization of the maximum individual regret/gaps for prioritizing the improvement. In other words, min i S i emphasizes the maximum group utility, whereas min i R i emphasizes selecting minimum among the maximum individual regrets. Based on the above concepts, the compromiseranking algorithm VIKOR consists of the following steps. Step 1: Determine the best f j, and the worst f j values of all criterion functions, j = 1, 2,..., n. If we assume the jth function represents a benefit, then f j =max i f ij (or setting an aspired level) and f j = min i f ij (or setting a tolerable level). Alternatively, if we assume the jth function represents a cost/risk, then f j =min i f ij (or setting an aspired level) and f j = max i f ij (or setting a tolerable level). * * Si S Ri R Q (1 ) i * * S S R R (6) * Where, S Mini Si, S Maxi S, * i R Mini Ri R Max R and 0 v 1, where v is, i i introduced as a weight for the strategy of maximum group utility, whereas is the weight of the individual regret. In other words, when v > 0.5, this represents a decisionmaking process that could use the strategy of maximum group utility (i.e. if v is big, group utility is emphasized), or by consensus when, or with veto when v < 0.5 ( Opricovic,1998 & Kackar 1985). Step 4: Rank the alternatives, sorting by the value of {S i, R i, and Q i i =1, 2,...,m}, in decreasing order. Propose as a compromise the alternative (A (1) ) which is ranked first by the measure min{q i i = 1, 2,...,m} if the following two conditions are satisfied (Huang et al., 2009): C 1. Acceptable advantage: Q(A (2) (1) ) 1/(m1), where A (2) is the alternative with second position in the ranking list by Q; m is the number of alternatives. C2. Acceptable stability in decision making: Alternative A (1) must also be the bestranked by {S i or/and R i i = 1, 2,...,m}. If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: 1739
28 A. Jalili, K. Shahriar, A. Sadri Alternatives A (1) and A (2) if only condition C 2 is not satisfied. Alternatives A (1),A (2),..., A (M) if condition C 1 is not satisfied. A (M) is determined by the relation Q(A (M) ) Q(A (1) ) < 1/(m 1) for maximum M (the positions of these alternatives are close. The compromise solution is determined by the compromiseranking method; the obtained compromise solution could be accepted by the decision makers because it provides maximum group utility of the majority (represented by min S, Eq. (4)), and minimum individual regret of the opponent (represented by min R, Eq. (5)). The VIKOR algorithm determines the weight stability intervals for the obtained compromise solution with the input weights given by the experts.( Opricovic, 1998) 3 FUZZY LOGIC A linguistic variable is defined as a variable whose values are not numbers, but words or sentences in natural or artificial languages. The concept of a linguistic variable appears as useful means for providing approximate characterization of phenomena that are too complex or illdefined to be described in conventional quantitative terms (Zadeh, 1965). The use of linguistic variables enables Decision Makers (DMs) to specify both the importance associated with each of a set of criteria, and the preference with respect to a number of strategic criteria which impact the selection and justification of several alternatives. The value of a linguistic variable can be quantified and extended to mathematical operations using fuzzy set theory (Zadeh, 1975). A fuzzy number is a special fuzzy set F = {x R f (x) }, where x takes its values on 1 the real line 1 and f (x) is a continuous mapping from to the close interval [0,1]. A triangular fuzzy number can be denoted as A=[a 1,a 2,a 3 ] (where and a 1,a 2,a 3 R ) 1 and its membership function f A( x ) : [0, 1] can be given as: ( x a1 ) / ( a2 a1) f A( x) ( x a3) / ( a2 a3) 0 Otherwise where b 1 2 3, b 1 and b 3 stand for the lower and upper value of the support of A, respectively, and b is the midvalue of A. The main operational laws for two triangular fuzzy numbers A =[a 1,a 2,a 3 ] and B =[b 1,b 2,b 3 ] and one no fuzzy number n=[n 1,n 2,n 3 ] are as follows (Kaufmann & Gupta, 1991): 3.1 Defuzzification ( A B) [ a b, a b, a b ] ( A! B) [ a b, a b, a b ] ( A B) [ a b, a b, a b ] ( A n) [ a n, a n, a n ] Fuzzy numbers can be regarded as systems with numerical input and numerical output. Internally these systems work with fuzzy values, which have to be mapped to nonfuzzy (crisp) values after processing. This conversion is called defuzzification. In this paper the mean value method is used for defuzzification. A fuzzy number A =[a 1i,a 2i,a 3i ] can always be given by its corresponding left and right representation of each degree of membership: 1740
29 23 rd Figure 1.A triangular fuzzy number A i Mean value method for defuzzification: 1 S A i S L A i S R A i (7) 2 S A a f x a f x ( S A a2i a3i 1 2 ( ) 2 i ( ) 2 i a i f i i (8) a1 i a2i 4 FUZZY VIKOR TECHNIQUE Assumptions and method steps are as follows: K = Number of decision makers, where K=1, 2,,k. i= Number of alternatives, where i=1, 2,,m. j= Number of criteria, where j=1, 2,,n. Step 1: Making matrix of criteria decision makers. Form a group of decision makers, determine the evaluation criteria and feasible alternatives. k decision makers use the linguistic variables, such as very low, low, medium, high and very high (the corresponding fuzzy numbers of linguistic terms are shown in Table 1) to assess the importance weight of criteria. Triangular fuzzy numbers for importance weight of the criteria are shown in Figure 2. Hence the matrix of criteria decision makers can be written as Figure 3. Figure 2. Triangular fuzzy numbers for importance weight of the criteria Table 1. Linguistic variables for the importance weight of criteria Symbol Linguistic terms Triangular fuzzy number very high L M R (,, ) high L M R (,, ) medium L M R (,, ) low L M R (,, ) very low L M R (,, ) D D D 1 2 D k C x x x 1 C2 x x x C x x x j x1 1 k x2 2 k 2 n n1 n2 xnk n Figure 3. Matrix of criteria decision makers x jk The rating of the criteria C j with respect to decision maker D k. j is the importance weight of the jth criterion holds. w k is the importance weight of decision makers opinions, where wk [0,1]. 1741
30 A. Jalili, K. Shahriar, A. Sadri min x, x,, x, M M M j w 1 x j 1 w 2 x j 2 w k x jk, maxx 1 2 R R R j, x j,, x jk L 1 L 2 L j x j x jk (9) Step 2: Making matrix of decision makersalternatives criteria. Identify the appropriate linguistic variables for evaluating the importance weight of criteria, and the rating of alternatives. K decisionmakers use linguistic variables: very poor, poor, medium, good and very good (the corresponding fuzzy numbers of linguistic terms are shown in Table 2) to evaluate the rating of m candidates in n criteria. Triangular fuzzy numbers for the rating of alternative are shown in Figure 4. Table 2. Linguistic variables for the rating of alternative Symbol Linguistic terms Triangular fuzzy number L M R very good (,, ) good ( L, M, R ) L M R medium (,, ) L M R poor (,, ) L M R x very poor x ( x, x, x ) Figure 4. Triangular fuzzy numbers for the rating of alternative Hence the matrix of decision makersalternatives criteria and the fuzzy decision matrix can be written as Table 3. Step 3: combination of matrix of decision makers criteria and decision makersalternatives criteria. with the relation Eq.(10). Z (min y,..., y, w x... w x, L L m m ij 1ij kij 1 1ij k kij R 1ij R max y,..., y ) kij (10) Z ij : A Fuzzy Variable of the ith alternative according to jth criteria. Table 3. Matrix of decision makersalternatives criteria C1 C2 Cn D1 A n A n Am 1m1 1m2 1mn D2 A n A n Am 2m1 2m2 2mn Dk A1 k11 k12 k1n A2 k 21 k 22 k 2n Am km1 km2 kmn 1742
31 23 rd Table 4. Aggregated triangular fuzzy number decision matrix A 1 A 2 A m C 1 1 Z11 Z 21 Z m1 C 2 2 Z12 Z 22 Z m2 Step 4: Defuzzification C n n Z1n Z 2n Z mn Convert fuzzy number to non fuzzy number (with using the relations Eq.(7 & 8)). The result of this step is given in Table 5. Step 5: Determine the best f j, and the worst f j values of all criterion functions, j=1, 2,..., n. If we assume the jth function Table 5. Non fuzzy number decision matrix A A A i 2 m C 1 1 f f f m1 C 2 2 f f f m2 represents a benefit, then f j =max i f ij (or setting an aspired level) and f j = min i f ij (or setting a tolerable level). Alternatively, if we assume the jth function represents a cost/risk, then f j =min i f ij (or setting an aspired level) and f j = max i f ij (or setting a tolerable level). Step 6: Compute the values S i and R i, i = 1, 2,...,m, using the relations Eq.(4) & (5). Step 7: Compute the Q j values for i=1,2,,m with the relation Eq.(6). C n n f 1n f 2n f mn Step 8: Rank the alternatives, sorting by the value of {S i, R i, and Q i i =1, 2,...,m}, in decreasing order. Step 9: Propose as a compromise the alternative (A (1) ) which is ranked first by the measure min{q i i = 1, 2,...,m} if the following two conditions are satisfied (Huang et al., 2009). C 1. Acceptable advantage: Q(A (2) )Q(A (1) ) 1/(m1), where A (2) is the alternative with second position in the ranking list by Q; m is the number of alternatives. C 2. Acceptable stability in decision making: Alternative A (1) must also be the bestranked by {S i or/and R i i = 1, 2,...,m}. If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: Alternatives A (1) and A (2) if only condition C 2 is not satisfied. Alternatives A (1),A (2),..., A (M) if condition C 1 is not satisfied. A (M) is determined by the relation Q(A (M) ) Q(A (1) ) < 1/(m 1) for maximum M (the positions of these alternatives are close). 5 CASE STUDY The purpose of this paper is to selection of the optimum underground mining method for Jajarm Bauxite Mine, using data obtained from the mine site. 5.1 Selection of Criteria There are too many factors affecting mining method selection such as spatial characteristics of the deposit, geologic and hydrologic conditions, geotechnical properties, economic considerations, technological factors and environmental concerns. Main criteria and their subcriteria are mentioned follows (Hartman and Mutmansky, 2002): (a) Spatial characteristics of the deposit such as general shape, plunge, dip, depth, 1743
32 A. Jalili, K. Shahriar, A. Sadri ore thickness existence of previous mining. (b) Geologic and hydrologic conditions such as mineralogy and petrography, chemical composition, deposit structure, uniformity of grade, alteration and weathered zones, and existence of strata gases. (c) Geotechnical properties such as elastic properties, plastic or viscoelastic behavior, state of stress, rock mass rating and other physical properties affecting competence. (d) Economic considerations such as reserves, production rate, mine life, productivity, comparative mining costs and comparative capital costs. (e) Technological factors such as recovery, dilution, flexibility of the method to changing conditions, selectivity of the method, concentration or dispersion of workings, ability to mechanize and automate and capital and labor intensities. (f) Environmental concerns such as ground control to maintain integrity of openings, subsidence or caving effects at the surface, atmospheric control, availability of suitable waste disposal areas, workforce and comparative safety conditions of the suitable mining methods. According to this criterion, 12 criteria having the most important are selected in Jajarm mine which are shown in Table 6. Table 6. Important creteria Symbol C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 Criteria Deposite thikness Deposite dip Deposite shape RMR of hangingwall RMR of ore RMR of footwall Depth Recovery C 9 C 10 C 11 C 12 Production Ore grade Ore uniformity Dilution 5.2 Candidate Mining Methods According to the mine and ore body conditions, five mining methods that are possible and appropriate to this mine, considered. These mining methods are given in Table 7. Table 7. Candidate mining methods Symbol SHS CFS SS SLS BM Method Shrinkage stoping Cut & fill stoping Stull stoping Sublevel stoping Bench mining 5.3 Fuzzy VIKOR technique for selection of optimum underground mining method Step 1: Form a group of decision makers; determine the evaluation criteria and feasible alternatives. Step 2: Identify the appropriate linguistic variables for evaluating the importance weight of criteria, and the rating of alternatives. Step 3: Aggregated triangular fuzzy number decision matrix. (Table 8) Step 4: Defuzzification Convert fuzzy number to nonfuzzy number. (Table 9) Step 5: Determine the best f j, and the worst f j values of all criterion functions, j = 1, 2,..., n (Table 10). 1744
33 23 rd Table 8. Aggregated triangular fuzzy number decision matrix j SHS CFS SS SLS BM C 1 (0.9,1,1) (0.1,0.44,1) (0.9,1,1) (0,0.44,1) (0.1,0.34,0.7) (0,0,0.1) C 2 (0.5,0.75,1) (0.1,0.54,1) (0.3,0.66,1) (0,0.41,1) (0.1,0.54,1) (0.1,0.34,0.7) C 3 (0.5,0.85,1) (0.3,0.5,0.7) (0.3,0.6,1) (0,0.41,1) (0,0.06,0.5) (0.1,0.4,0.7) C 4 (0.1,0.52,0.9) (0.1,0.3,0.5) (0.1,0.38,0.9) (0.1,0.3,0.5) (0.1,0.34,0.7) (0.1,0.3,0.5) C 5 (0,0.15,0.7) (0.1,0.3,0.5) (0,0.15,0.5) (0,0,0.1) (0.1,0.65,1) (0,0,0.1) C 6 (0.9,1,1) (0,0.24,0.5) (0.1,0.52,0.9) (0,0.24,0.5) (0,0.3,0.7) (0.1,0.3,0.5) C 7 (0.3,0.56,0.9) (0,0.25,0.7) (0.1,0.56,0.9) (0,0.15,0.5) (0.1,0.46,0.9) (0,0,0.1) C 8 (0.3,0.64,0.0.9) (0.1,0.3,0.5) (0.5,0.91,1) (0,0,0.1) (0.1,0.3,0.5) (0,0,0.1) C 9 (0.3,0.85,1) (0,0,0.1) (0.5,0.7,0.9) (0,0.21,0.5) (0.1,0.15,0.5) (0,0,0.1) C 10 (0.3,0.66,1) (0.1,0.4,0.7) (0.5,0.7,0.9) (0,0.31,0.9) (0,0.35,0.9) (0.1,0.3,0.5) C 11 (0.5,0.85,1) (0.1,0.3,0.5) (0.1,0.3,0.5) (0.1,0.3,0.5) (0.1,0.3,0.5) (0.1,0.21,0.5) C 12 (0.1,0.44,1) (0.1,0.36,0.7) (0.5,0.7,0.9) (0,0.09,0.5) (0.1,0.3,0.5) (0,0,0.1) Table 9. Non fuzzy number decision matrix j SHS CFS SS SLS BM C C C C C C C C C C C C Table 10. Determine the best f j, and the worst f j values of all criterion functions, j = 1, 2,..., n. C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 f j f j Step 6: Compute the values S i and R i, i = 1, 2,...,m (Table 11). Step 7: Compute the Q j values for i=1,2,,m (Table 12) Step 8: Rank the alternatives, sorting by the value of {S i, R i, and Q i i =1, 2,...,m}, in decreasing order (Table 13). Table 11. Index S i and R i SHS CFS SS SLS BM S i R i Table 12. Index Q i SHS CFS SS SLS BM Q i
34 A. Jalili, K. Shahriar, A. Sadri Table 13. Rank the alternatives S i CFS SLS SHS SS BM R i CFS SLS SHS SS BM Q i CFS SLS SHS SS BM Step 9: conditions Since the Q(A (2) )Q(A (1) ) ( , Alternative A (1) also be the bestranked by {S i or/and R i i = 1, 2,...,m}. Hence alternative A (1) or cut and fill stoping method is optimum underground mining method for the mine under question. 6 CONCLUSION There is no single appropriate mining method for a deposit. Usually, two or more feasible methods are possible and each method entails some inherent problems. Consequently, the optimal method is one that offers the least problems. Selection of an appropriate mining method is a complex task that requires consideration of many technical, economical, political, social, and historical factors. The appropriate mining method is that which is technically feasible for the ore geometry and ground conditions, while being a lowcost operation. In this paper using fuzzy VIKOR method, the degree of importance of the effective factors on the model was investigated. As a result, using this approach the cut and fill stoping method was selected as optimum underground mining method in Jajarm Bauxite Mine. REFERENCES Alpay, S., & Yavuz, M., Underground mining method selection by decision making tools, Tunnelling and Underground Space Technology, 24, pp Chen, M.F., Tzeng, G.H., & Ding, C.G., Fuzzy MCDM approach to select service provider, In IEEE international conference on fuzzy systems, pp Chen, Y.C., Lien, H.P., Tzeng, G.H., & Yang, L.S., Fuzzy MCDM approach for selecting the best environmentwatershed plan, Applied Soft Computing, 11, pp Deng, H., Yeh, C.H., & Willis, R.J., Intercompany comparison using modified TOPSIS with objective weights, Computers and Operations Research, 27, pp Hartman, H.L., & Mutmansky, J.M., Introductory Mining Engineering, John Wiley, New Jersey. Huang, J.J., Tzeng, G.H., & Liu, H.H., A Revised VIKOR Model for Multiple Criteria Decision Making  The Perspective of Regret Theory, In: Shi, Y. et al (Eds.) CuttingEdge Research Topics on Multiple Criteria Decision Making. Springer, Berlin Heidelberg, pp Kackar, R.N., Offline quality control, parameter design and the Taguchi method, Journal of Quality Technology, 17, pp Kaufmann, A., Gupta, M.M., Introduction to Fuzzy Arithmetic Theory and Applications, Van Nostrand Reinhold, New York. Naghadehi. M.Z, Ataei,M., The application of fuzzy analytic hierarchy process (FAHP) approach to selection of optimum underground mining method for Jajarm Bauxite Mine, Expert Systems with Applications, 36, pp Opricovic, S., Multicriteria optimization of civil engineering systems, Faculty of Civil Engineering, Belgrade. Opricovic, S., & Tzeng, G.H., Multicriteria planning of postearthquake sustainable reconstruction, ComputerAided Civil and Infrastructure Engineering, 17, pp Opricovic, S., & Tzeng, G.H., Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research 156, pp Wang, T. C., & Lee, H. D., Developing a fuzzy TOPSIS approach based on subjective weights and objective weights, Expert Systems with Applications, 36, pp Chiu, W.C., & Tzeng, G.H., A new hybrid MCDM model combining DANP with VIKOR to improve estore business, KnowledgeBased Systems. Zadeh, L.A., Fuzzy sets, Information and Control, 8, pp Zadeh, L.A., The concept of a linguistic variable and its applications to approximate reasoning, Part I, Inf. Sci. 8,pp , Part II, 8, pp ; Part III, 9, pp
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59 23 rd The Impact of Interaction between Mine Facility Location Selection Criteria on Final Ranking of Site Alternatives M. Fazeli, M. Osanloo Amirkabir University of Technology, Faculty of Mining and Metallurgical Engineering, 424 Hafez Ave, Tehran, Iran, , ABSTRACT Mine Facility Location Selection (MFLS) is one of the most commonly encountered problems in open pit mine planning and design in line with sustainable development. This is a critical decision which must be simultaneously considered a number of criteria such as economical parameters, environmental aspect, stability condition, technical factors, socialeconomic and facility characteristics to find the best location among feasible alternatives. Likewise, according to the sophisticated structure of the problem, imprecise data, lack of sufficient information, and inherent uncertainty, the usage of the fuzzy sets can be useful to solve this problem. The aim of this study is to propose a new hybrid Fuzzy Multi Attribute Decision Making (FMADM) model considering interaction between mine facility location selection effective criteria. In this paper Fuzzy Analytical Network Process (FANP) has been used to calculate the interaction between attributes and combination of Fuzzy Analytical Hierarchy Process (FAHP), FANP and entropy applied for obtaining the overall precise weight of attributes. Proposed model analysis showed that considering the interdependency of criteria changes the final weight of attributes. The proposed model has been applied for processing plant location selection of Sangan open pit mine of Iran. 1 INTRODUCTION The purpose of mining is to meet the demands of metals and industrial minerals of human to develop infrastructure and improve the quality of life of the population. The extracted substances are in many cases the raw materials for the manufacture of many goods and materials (Kumral et al. 2008). The increasing demand and ascending price of minerals in many cases make it possible to process lower grade ores, which means more production of material and more environmental disturbance. Nowadays it is believed that the public expect the mining industry to care the environmental issues and try to eliminate the adverse environmental impacts or at least minimize the intensity as well as the extent of them. Sustainable development requirements finally lead to using improved and environmentally friendly technologies. Using sustainable development principles must be started at the beginning of the project by selecting suitable locations for mine facility installation. To put mining operation in line with sustainable development throughout its life and also after mine closure especial arrangements must be made (Naraei et al. 2011). Mine planning and design are very complex engineering subjects and require engineering knowledge and good understanding of many issues. One of the most important issues is decision making about MFLS. The goal of MFLS is to find the best location that should comply with sustainable development principles so as to 1771
60 M. Fazeli, M. Osanloo ensure sustainable development of mine and unify economic, social and the environmental efficiency. MFLS is a very important decision for mining companies because it is costly and difficult to reverse, and it entails a long term commitment so that, a poor choice of location might result in excessive transportation costs, adverse environmental impacts, or some similar conditions that would be detrimental to mining activities (Stevenson 1993). In the past, MFLS was a simple procedure on the basis of economic criteria and ease of operation. The process was to estimate the costs for each alternative, and the lowest cost alternative would ordinarily be the hands down winner (Caldewell et al. 1983, Robertson 1982 & Magda 1985), but effect of multiple criteria on MFLS makes it complex as the conventional procedures therein would result in incorrect results. Thus, the MFLS can be viewed as a multi attribute decision making (MADM) problem that helps decision makers select the most preferable decision and provide the basis of a decision support system. In MADM problem, a decision maker has to choose the best alternative that satisfies the evaluation criteria among a set of candidate solutions. In classical MADM methods ratings and the weights of the criteria are known precisely, whereas in the real world, in an imprecise and uncertain environment, it is an unrealistic assumption that the knowledge and representation of a decision maker or expert are so precise. The fuzzy set theory could resemble human reasoning in use of approximate information and uncertainty to generate decisions. It was specifically designed to mathematically represent uncertainty and vagueness and provide formalized tools for dealing with the imprecision intrinsic to many problems (Zadeh 1965). There is no well to consider the weight of MFLS criteria on final ranking of site alternatives, because not only various options should be considered as potential locations, but also there are a large number of effective which are in conflict with each other. The articles listed in Table 1 address some different type of facility location selection models in the context of MADM in the recent years and weighting methods containing their advantages and disadvantages. Based on Table 1, there are many shortcomings to these models that have been used for facility location selection, among them limitation in variety of attributes such as weakness in usage of linguistic and fuzzy attributes, ignoring the interdependency of attributes and ignoring entropy in decision matrix are the most important shortcomings that have been considered in this study. The main objective of this paper is to present a powerful fuzzy MADM tool for making an appropriate decision in complex problems featuring uncertainty and contradictory goals. To make this study more sensible and gain a more representative description of MADM process, we would apply a hybrid model of FAHP, FANP and entropy to weight MFLS criteria. FAHP is an application of the combination of Analytic Hierarch Process and fuzzy set that the linguistic scale of traditional AHP method could express the fuzzy uncertainty when a decision maker making a decision. Moreover, ANP would apply to calculate the interdependency between attributes. The proposed model is able to calculate and consider entropy in decision matrix. Finally, the processing plant location of Sangan open pit mine of Iran was selected using the TOPSIS method under a fuzzy environment due to its rational structure, simplicity, good computational efficiency and capability to determine the relative performance for each option in a simple mathematical form. 2 BASIC OF FUZZY SET THEORY Uncertainty is a major part of decision making problems in real world that is resulted from two areas (Fouladgar et al. 2011): (1) uncertainty in subjective judgments (2) uncertainty due to lack of data or incomplete information. The first is due to first is due to expert judgment. He/she may not be 100% sure when making subjective 1772
61 23 rd Table 1. Facility location selection methods and weighting methods (advantages and disadvantages) Author Year Ranking method Weighting method Subjective Pairwise ANP Objective Entropy No limitation in number of alternatives No limitation in number of attributes No limitation in Variety of attributes (fuzzy, linguistic, crisp) Considering the interdependency between criteria Osanloo 2003 SAW Akbari 2007 AHP Hekmat 2007 FAHP Shahriar 2007 Yager Hekmat 2008 SAW, AHP,TOPSIS Yavuz 2008 Yager Ataei 2008 ELECTRE Golestanifar 2008 FTOPSIS, FuzzyWP Athawale 2010 PROMETHEE II Yazdani 2012 FVIKOR Anand 2012 ANP Considering Entropy in decision matrix judgments. The second one is caused by insufficient information of some attributes The fuzzy set theory, introduced by Zadeh (1965), deal with vague, imprecise and uncertain problems. A fuzzy set is a class of objects with continuum of grades of membership. Such a set is characterized by a membership function, which assigns to each object a grade of membership ranging between zero and one. 2.1 Linguistic Variables A linguistic variable is a variable whose values are words or sentences in a natural or artificial language and provides a means of approximate characterization of phenomena which are too complex to be amenable to description in conventional quantitative terms. The main applications of the linguistic approach lie in the realm of humanistic systems (Zadeh 1975). 2.2 Fuzzy Numbers A fuzzy number M is a convex normalized fuzzy set M of the real line R such that: It exists such that one x0 R with x 1 M 0 ( x 0 is called mean value of M ).  x is piecewise continuous. M In this paper, we use Triangular Fuzzy Numbers (TFNs) because of their computational simplicity and they are useful in promoting representation and information processing in a fuzzy environment. There are various operations on TFNs. Here, only important operations used in this study are illustrated. If we define, two positive TFNs M l, m, u and M l, m, u then: Inverse: 12 Addition: 23 Multiplication: 34 Division: M (1/ u, m l (1/,1/,1/ ) M M ( l l, m m, u u ) M M ( l. l, m. m, u. u ) M 1 % M 1 l 1 / u 2, m1 / m2, u1 / l2) The distance between two triangular fuzzy numbers can be calculated by vertex method as follow: 1 d M M l l m m u u v 3, (1) An important concept related to fuzzy numbers application is defuzzification. This study adopted the simple center of gravity method which converts a TFN into a crisp value as follows: X M 1 ( l, m, u ) / 3 Where X M is a crisp value. 3 PROPOSED METHODOLOGY OF MFLS (2) The general procedure for MFLS in this paper divided into the following steps: 1 Determination of MFLS criteria and their interdependency 2 Determination of criteria weight by hybrid model 1773
62 M. Fazeli, M. Osanloo 3 Alternatives evaluation and ranking procedure by FTOPSIS (Fig. 1) Figure 1. Mine Facility Location Selection (MFLS) framework 3.1 Determination of MFLS criteria and their interdependence There are many criteria that influence the MFLS process. In assessing a site as a possible location for mine facilities, many factors should be considered. These factors may be presented in many ways; however, the most useful way is the one that may be easily understood by the community (Tchobanoglous et al. 1993). The number and significance of these factors can be different for each mine in each country because the process of MFLS involves a number of stakeholders and sets of requirements such as legislation, restrictions, rules, local expertise and experience. In our study fifty four numbers of extracted leading evaluative attributes from comprehensive literature review, advices by experts and sustainable development framework introduced by Azapagic (2004) are grouped into six main categories, including (1) Economic parameters, (2) Stability conditions, (3) Socialeconomic factors, (4) Technical parameters, (5) Environmental concerns, and (6) Facility characteristic, then, each main category was protracted to subs criteria as shown in Figure 2. Based on the literature review in introduction, in existing methods, the influence of each criterion is verified separately and the interdependency between criteria is ignored. For example, the parameters distance from pit and environmental impacts are simultaneously effective on selecting site No. 1. As the distance from pit increases, the operational costs will also increase; thus, the probability of choosing site No. 1 decreases. On the other hand, increasing distance from pit can be compensated by eliminating the adverse environmental impacts or at least minimizing the intensity and the extent of them. In this condition site No. 1 may be preferred. This paper has discussed how to determine the interdependency between criteria in fuzzy environment. 3.2 Determination Criteria Weight by Hybrid Model Since the criteria of evaluation have diverse significance and meanings, we cannot assume that each criterion has equal importance. Weighting methods try to define the importance of each criterion in decision making process. Changing the weight in decision making process has a great influence on ranking results. There are many methods that can be employed to determine the weights of criteria, such as the eigenvector, weighted least square method, entropy, AHP, ANP and linear programming techniques for multidimensional analysis of preference (LINMAP). Since in decision making problems, there are a direct access to the values of the decision matrix, the entropy and LINMAP methods can be commensurate. Entropy and LINMAP methods both work based on a decision matrix, whereas AHP, ANP, eigenvector method, and weighted least square method follow a set of judgment based pairwise comparison matrices. The selection of a method depends on the nature of the problem. These methods were neither enough nor complete, as it is not possible to design a methodology that will present a perfect weight for each criterion. In this study; a hybrid model based on entropy, FANP and FAHP methods used to obtain the overall fuzzy weight of each criterion. The 1774
63 23 rd Figure 2. Structure of MFLS hierarchy overall fuzzy weight of each criterion W * j divides into the: 1 Entropy weight ( W j ) based on a decision matrix. 2 FAHP weight with interdependency between criteria for fuzzy data ( j ). The first step is to calculate the weights based on a decision matrix. The speed of the LINMAP method is, however, lower than the entropy method. Furthermore, using the entropy method, it is possible to combine the other weights (Samimi et al. 2012). In the second step FAHP and FANP was used to calculate the relative importance and interdependency between criteria given by experts in pairs. As for the experts opinions, this study adopted the Similarity Aggregation Method (SAM) proposed by Hsu and Chen (1996) to integrate experts weight values for various evaluation criteria. Moreover, ANP is used because there are nonlinear relationships among hierarchical levels which make some problems in implementation of AHP method. Eventually, a set of entropy weights ( W j ) that transform to nine level, fuzzy linguistic variables ( W j ) and AHP weights with interdependency between criteria ( ), can be used to determine the overall fuzzy weights ( W * j ) by using: W * j j W j 1,2,, n n j (3) W W j1 j j Entropy weighting Shannon and Weaver (1947) proposed the entropy concept for deciding the objective weights of attributes. Entropy weighting used to determine the importance weights of decision attributes by directly relating a criterion s importance weighting relative to the information transmitted by that criterion. For example, in a given decision matrix with column vector x j = (x 1j, x 2j,, x mj ) that shows the contrast of all alternatives with respect to jth attribute, an attribute has little significance when all alternatives have similar outcomes for that attribute. Mathematically this means that the projected outcomes of attribute j, P ij, are defined as: P ij x ij m x i1 ij (4) The entropy E j of the set of projected outcomes of attribute j is: m E j (1 ln m) P 1 ij ln P i (5) ij Where m is the number of alternatives and guarantees that E j lies between zero and one. d j of the information provided by outcomes of attribute j as d j 1 E j. Hence, the entropy weighting of an attribute is calculated as follows: W d d n (6) j j j In situations 1 j where a decision maker has an priori subjective weighting for j 1775
64 M. Fazeli, M. Osanloo * attribute, a compromise weighting, W, that j take into account both an expert s opinion and the objective entropy weighting of the attribute is calculated as follows: * n j j j j 1 j j W W W j 1,2,, n Weighting with FAHP (7) This method has been developed by Saaty and Vargas (1994) that is a mathematical tool for solving the MADM problems. For a matrix of order n, ((n) (n  1)/2) comparisons are required. The fundamental scale used for this purpose is based on Saaty 19 scale. AHP method is combined with fuzzy set to solve the problem of the conventional AHP in handling uncertainty. For achieving the aim, a scale of 1 9 can be defined for TFNs instead of traditional scale1 9, as presented in Table 2. Table 2. The definition of fuzzy number Intensity of importance Fuzzy number Linguistic variable 9 = (8,9,9) Perfect (P) 8 (7,8,9) Absolute (A) 7 = (6,7,8) Very Good (VG) 6 = (5,6,7) Fairly Good (FG) 5 = (4,5,6) Good (g) 4 = (3,4,5) Preferable (PR) 3 = (2,3,4) Not Bad (N) 2 = (1,2,3) Weak advantage (W) 1 = (1,1,1) Equal (E) This section calculated the weight value of criteria w j by Column Vector Geometric Mean Method proposed by Buckley, because the steps of this approach are relatively easier, less time taking and less computational expense than the other fuzzy AHP. Z a 1 a 2 a i j n w Z ( Z Z Z ), i, j 1, 2,, n n ( 1/n i a i 1 a i 2 aij ),, 1, 2,,. Z % j i (Z Z 1 Z 2 n (8) (9) Where the column vector mean value of fuzzy number is Z i and the weight of No. i criterion is w j. w j Weighting with FANP The Analytical Network Process is one of the most comprehensive frameworks for the analysis of corporate decisions. It allows both interaction and feedback within clusters of elements (interdependency). ANP introduced by Saaty (1996), is a generalization of the AHP to generate priorities for decisions without making assumption about a unidirectional hierarchy relationship among decision levels. The major difference between AHP and ANP is that ANP is capable of handling interdependency between the decision levels and attributes. Because there is a high degree of interdependency between MFLS criteria, this study adopted the Fuzzy ANP (FANP) method to calculate the relative importance of the evaluation criteria. The weighting by FANP can be divided into three steps, which are described as follows: Step 1: Without assuming the interdependency between criteria, the expert is asked to weight all proposed criteria with FAHP method described earlier. The result of the SAM and FAHP methods on n criteria can be summarized in a weight vector ( w j ) with the help of Equations 89. Step 2: The effects of the interdependency between the criteria are resolved. The expert will examine the impact of all criteria on each other by pairwise comparisons as in AHP method. A couple of questions such as: which criterion will influence criterion C 2 more; C 3 or C 5? And how much more? are answered. For achieving the aim, a scale of 1 9 can be defined for TFNs (Tab. 2) and 0 where C 3 and C 5 is independent of C 2. Various pairwise comparison matrices are constructed for each criterion C k as follow: C [ C ] ( 1) ( 1), k 1, 2,, n C k C k ( n 1) ( n 1) (10) The local weight vectors for these matrices are calculated by using Column Vector Geometric Mean Method proposed by Buckley and shown as column components in fuzzy interdependency weight matrix ( w ' ). Step 3: Now we can obtain the interdependency priorities of the MFLS criteria by synthesizing the results from previous two steps as follow: j ' w ( w j ), j 1,2,, n (11) 1776
65 23 rd Finally, the overall fuzzy weights of evaluation criteria can be determined by Equation 3. 4 ALTERNATIVES EVALUATION AND RANKING PROCEDURE The full ANP and AHP solution is only partially usable if the number of criteria and alternatives is low. In this paper, we use FTOPSIS and apply it to achieve the final ranking result to avoid a large number of pairwise comparisons and also four advantages addressed earlier. Also, the basic concept of this method is that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from negative ideal solution. Positive ideal solution is a solution that maximizes the benefit criteria and minimizes cost criteria, whereas the negative ideal solution maximizes the cost criteria and minimizes the benefit criteria. Therefore, this method is suitable for cautious (risk avoider) decision maker(s), because the decision maker(s) might like to have a decision which not only makes as much profit as possible, but also avoids as much risk as possible. So it is suitable for those situations in which the decision maker wants to have maximum profit and also the risk of the decisions is important for him/her (Aghajani et al. 2011). 4.1 Fuzzy TOPSIS method The TOPSIS method is a technique to calculate the preferences by similarity to ideal solution and it was proposed by Hwang and Yoon (1981). In the classical TOPSIS method, the weights of the criteria and the ratings of alternatives are known precisely and crisp values are used in the evaluation process. However, under many conditions crisp data are inadequate to model real life decision problems. In such cases, the FTOPSIS method is proposed where the weights of criteria and ratings of alternatives are evaluated by linguistic variables represented by fuzzy numbers to deal with the deficiency of the traditional TOPSIS. In general, a MADM problem can be concisely expressed in matrix format as: (12) Where possible alternatives are A 1, A 2,, An, C1, C2,, Cn are criteria which measure the performance of alternatives and x ij is the rating of alternative A i with respect to criterion C j which could be in three main types of information (linguistic terms, fuzzy numbers and deterministic data). The step of FTOPSIS method can be defined as follow (Chen, 2000): Step 1: Construct the normalized decision matrix R The first step concerns the normalization of the judgment matrix D x ij. Generally there are two kinds of attributes, the benefit type and the cost type. The higher the benefit type value is, the better it will be. While for the cost type, it is the opposite. This study adopts normalization methods for deterministic number, triangle fuzzy number and linguistic terms that introduced by Aghajani (2011): Deterministic numbers normalization Let r ij be the normalized form of the number k ij, then for benefit index, we have: r k max k ij ij ij j And for cost index: r min k k ij ij ij j (13) (14) Triangular fuzzy number normalization Let r L, M, U ij rij r ij be the normalized form of the triangle fuzzy number k L, M, U ij kij k ij, then for benefit index, we have: L M U kij kij k ij,,, 1 i m, j I U U U 1 max kij max kij max k ij j j j And for cost index: L L L min kij min kij min k ij j j j,,, 1 i m, j I U M L kij kij k ij 2 (15) (16) 1777
66 M. Fazeli, M. Osanloo Where I 1 associated with the benefit criteria and I 2 associated with the cost criteria. With benefit and cost attributes, we discriminate between criteria that the decision maker desire to maximize or minimize, respectively Linguistic terms normalization Linguistic terms can be transferred into TFNs, then use the Equations to normalize them. Table 3 is applied to transform linguistic terms into TFNs. Table 3. Transformation linguistic terms to triangular fuzzy numbers The normalized decision matrix is as follows: R r ij, i 1, 2,, m, j 1, 2,, n (17) Step 2: Constructing the weighted normalized decision matrix V * A set of weights W j, where W * j is the weight of the jth attribute, is incorporated to form the weighted normalized decision matrix V as follows: (18) Step 3: Define the Fuzzy Positive Ideal and the Fuzzy Negative Ideal Solutions Let us suppose that A identifies the fuzzy positive ideal solution (FPIS) and A the fuzzy negative ideal solution (FNIS). They are defined respectively as follows:, A v 1, v 2, v n, (19) v Max v, i 1,2,, m, j 1,2,, n j i ij A v, 1, v 2, v n, v Min v i 1,2,, m, j 1,2,, n j Linguistic terms i ij Triangle fuzzy numbers The worst (TW) (0.0,0.1,0.2) Worse (W) (0.1,0.2,0.3) Very bad (VB) (0.2,0.3,0.4) Bad (B) (0.3,0.4,0.5) Normal (N) (0.4,0.5,0.6) Good (G) (0.5,0.6,0.7) Very good (VG) (0.6,0.7,0.8) Better (BE) (0.7,0.8,0.9) The best (TB) (0.8,0.9,1.0) V r. w, i 1, 2,, m, j 1, 2,, n ij j (20) Step 4: Measure the distance between alternatives and ideal solutions To calculate the distance of each alternative from A and A the following equations can be easily adopted: n v ij, v j, S d v, v, i 1,2,, m (21) i ij j j1 n ij, j, S d v, v, i 1,2,, m (22) i ij j j1 d, is distance between two TFNs obtained from Equation (2). Step 5: Measure the relative closeness to ideal solution and final ranking The final ranking of alternatives is obtained by referring to the value of the relative closeness to the ideal solution, defined as follows: Si CC i, i 1,2,, m Si S (23) i According to the closeness coefficient, determine the ranking order of all alternatives. 5 EVALUATING MODEL APPLICATION AND RESULTS In order to verify the proposed model, the selection of a processing plant location of Sangan open pit mine of Iran was evaluated. Sangan iron mine project is located 16 km north of Sangan and 300 km southeastern of Mashhad in Khorasan Razavi province in Iran. Three feasible alternatives were selected for the processing plant installation using Geographical Information System. The locations of alternatives are shown in Figure 3 with letter A, B and C. These locations are entered into the model as alternatives. For this case we screened proper criteria by opinions of decision group. Finally, 10 main criteria involved in this selection include belt conveyor length (C 1 ), distance from railway (C 2 ), distance from tailing dam (C 3 ), preparation costs (C 4 ), distance to main roads (C 5 ), reclamation and closure costs (C 6 ), stability condition (C 7 ), socialeconomic factors (C 8 ), water contamination (C 9 ) and ecology disturbance C 10 ). These parameters are entered as criteria to the model (Tab. 4). Ten main criteria are considered in this case so that four of which are crisp values 1778
67 23 rd (C 1, C 2, C 3 and C 5 ), four of them are linguistic terms (C 7, C 8, C 9 and C 10 ) and others are fuzzy numbers (C 6 and C 4 ). In this process, stability condition and social economic factors are entered as benefit criteria (positive effect on decision making) and the other criteria are supposed as costs. between criteria. This section adopts SAM and FAHP to integrate experts opinions to obtain the relative importance of evaluation criteria given by experts in group decision (Fig. 5). Figure 5. Ranking of main criteria by SAM and FAHP Figure 3. Location of alternatives for the processing plant site ( A, B and C ) 5.1 Calculate criteria weights by entropy Using Table 4 and Equations 1316, normalized decision matrix calculated as Table 5. Due to complex calculations of entropy method for TFNs, traditional entropy method for deterministic number was applied in this step. Therefore, the simple center of gravity method applied, the results are shown in Figure Calculate interdependency between criteria by FANP In this section, the interdependency between the 10 main criteria is analyzed (Fig. 6). The experts will examine the impact of all criteria on each other by pairwise comparisons. Considering Figure 10, four pairwise comparison matrices for reclamation and closure costs, preparation costs, water contamination and ecology were developed. These criteria have dependency with other criteria. The local weight vectors for these matrices obtained by using column vector geometric mean method and shown as rows in matrix w ' (Tab. 6). Figure 4. Ranking of main criteria by entropy method ( 5.2 Calculate criteria weights by FAHP An evaluation team of six members included two mine planning engineers, two academic professors and two environmental agencies was used. In this case, the relative importance of experts is equal. Note that, experts construct pairwise comparison matrix without assuming the interdependency Figure 6. Main criteria interdependency network 5.4 Calculate FAHP weights with interdependency between criteria The relative importance of the criteria considering interdependence can now be obtained by multiplying the w j by the weight w j 1779
68 M. Fazeli, M. Osanloo Table 4. Evaluation value for processing plant location selection in hypothetical open pit mine C 1 (km) C 2 (km) C 3 (km) C 4 (M$) C 5 (km) C 6 (M$) C 7 C 8 C 9 C 10 A (1.95, 2.1, 2.25) 2.6 (0.19, 0.21, 0.23) VG N VB N B (2.44, 2.71, 3) 1.9 (0.22, 0.24, 0.26) N B B B C (2.25, 2.5, 2.75) 1.6 (0.21, 0.23, 0.25) N B B B Table 5. Normalized decision matrix C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 A (0.87,0.93,1.0) 0.62 (0.83,0.90,1.0) (0.75,0.88,1.0) (0.67,0.83,1.0) (0.5,0.67,1.0) (0.5,0.6,0.75) B (0.65,0.71,0.80) 0.84 (0.73,0.79,0.86) (0.5,0.63,0.75) (0.5,0.67,0.83) (0.4,0.5,0.67) (0.6,0.75,1.0) C (0.71,0.78,0.87) 1.0 (0.76, ) (0.5,0.63,0.75) (0.5,0.67,0.83) (0.4,0.5,0.67) (0.6,0.75,1.0) Table 6. Interdependency between criteria (matrix w ' j ) j Based on Figure 8, belt conveyor length, preparation costs and distance from railway are the most important criteria in processing plant location selection in Sangan open pit mine, followed by distance from main roads, distance from tailing dam, stability condition and water contamination. The priority of other criteria is reclamation and closure costs, ecology and social economic factors. of matrix w ' j based on Equation 11. The FAHP weights with interdependence between criteria are shown in Figure 7. Figure 8. Overall precise weights of criteria Figure 7. FAHP weights with interdependency of criteria 5.5 Calculate the overall weights of criteria The overall fuzzy weights ( W * j ) are obtained for each criterion by using Equation 3. The weight of each criterion includes entropy of decision matrix, weight of FAHP with considering interdependency between criteria by FANP. The final precise normalized weights of processing plant location selection criteria are illustrated in Figure 8. In order to illustrate and analyze the effect of interdependency of criteria the proposed model was solved without considering interdependency between them. To achieve this aim we assume that w j j (i.e. matrix w ' j do not formed), the results are shown in Figure 9. Figure 9. Criteria weights, (a) without considering interdependency of criteria (b) Considering interdependency of criteria 1780
69 23 rd 5.6 Final ranking of alternatives by FTOPSIS In this section ranking process via FTOPSIS put forward. First, decision matrix (Tab. 4) normalized (Tab. 5) and then, the weighted normalized fuzzy decision matrix for the alternatives is calculated using Equation 18. After a weighted normalized fuzzy decision matrix is formed, fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are determined using Equations Then the distance of each alternative from FPIS and FNIS with respect to each criterion is calculated using vertex method (Eq. 1). S i, S i and closeness coefficients of three alternatives are calculated by Equations 2123, results are shown in Table 7. Table 7: FTOPSIS analysis (considering interdependency of criteria) A B C FPIS FNIS Closeness coefficient Ranking According to the closeness coefficient of three alternatives (Tab. 7), the ranking order of three alternatives is determined as A > B > C. The first alternative (A) is determined as the most appropriate facility location for the processing plant installation. In other words, the first alternative is closer to the FPIS and farther from the FNIS. Finally, in order to illustrate the effect of interdependency between criteria on final ranking, closeness coefficient of three alternatives calculated without considering the interdependency between criteria, the ranking order of three alternatives is determined as B > C > A (Tab. 8). Table 8. FTOPSIS analysis (without considering interdependency of criteria) A B C FPIS FNIS Closeness coefficient Ranking CONCLUSION Mine facility location selection is a complex multi person, multi criteria decision problem while sustainable development challenges facing the minerals and metals industry need a comprehensive and interdisciplinary approach based upon reliable data and transparent methodical approaches. In assessing a site as a possible location for mine facilities, many factors should be considered. In this paper fifty four numbers of evaluative attributes are grouped into six main categories as shown in Figure 2. The main objective of this paper is to present a powerful fuzzy MADM tool for making an appropriate decision in MFLS problems featuring uncertainty and contradictory goals. In this approach, a hybrid model of FAHP, FANP and entropy was used to weight the criteria. SAM and FAHP were used to integrate experts opinions to obtain the significance evaluation of evaluation criteria given by experts in group decision. Moreover, FANP has been used to calculate the interdependency between attributes. The proposed model is able to calculate entropy in decision matrix. Finally, the processing plant location of Sangan open pit mine of Iran was selected using the TOPSIS method under a fuzzy environment. Proposed model analysis showed that considering the interdependency of criteria change the final weights of attributes (Fig. 9). As a result ignoring the interdependency of criteria can cause error in final decision making. REFERENCES Aghajani, A., Osanloo, M. & Karimi, B Deriving preference order of open pit mines equipment through MADM methods: application of modified VIKOR method, Expert Systems with Applications, 38, pp Akbari, A., Osanloo, M. & Hamidian, H Suggested method for tailing dam site selection with Analytical Hierarchy Processing (AHP): case study in coal washery tailing dam of Anjirtange plant SavadkoohIran, Proceeding of application of computers and operations research in the mineral industry (APCOM), Santiago, Chile, pp
70 M. Fazeli, M. Osanloo Anand, G., Kodali, R. & Dhanekul, C.S An application of Analytic Network Process for selection of a plant location: a case study, International Journal of Services and Operations Management (IJSOM), 12, 1, pp Ataei, M Selecting Alumina Cement plant location by ELECTRE approach. International Journal of Industrial Engineering and Production Management (IJIE) (International Journal of Engineering Science) (in Persian), 19, pp Athawale, V.M. & Chakraborty, S Facility location selection using PROMETHEE II method, International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, pp Azapagic, A Developing a framework for sustainable development indicators for the mining and minerals industry, Journal of cleaner production, pp Caldewell, J.A. & Robertson, A.M Selection of tailings impoundment sites. Die Sivielingenieur in SuidAfrica, pp Chen, C.T Extensions of the TOPSIS for group decision making under fuzzy environment. Fuzzy Sets System, 114, pp.19. Fouladgar, M.M., YazdaniChamzini, A. & Zavadskas, E.K An integrated model for prioritizing strategies of the Iranian mining sector. Technological and Economic Development of Economy, 17, pp Golestanifar, A. & Aghajani, A Group selection of waste dump site in open pit mines by using WDL algorithm in uncertainly condition, proceeding of the Seventh Iranian Students Conference of Mining Engineering, Sahand University, pp Hekmat, A., Osanloo, M. & Akbarpur Shirazi, M Waste dump site selection in open pit mines using fuzzy MADM algorithm, Proceedings of the Sixteenth International Symposium on Mine Planning and Equipment Selection (MPES), Thailand, pp Hekmat, A., Osanloo, M. & Shirazi, M.A New approach for selection of waste dump sites in open pit mines, Mining Science and Technology, 117, 1, pp Hsu, H. M. & Chen, C. T Aggregation of fuzzy opinions under group decision making. Fuzzy Sets and System, 79, pp Kumral, M. & Dimitrakopoulos, R Selection of waste dump sites using a tabu search algorithm, The Journal of the Southern African Institute of Mining and Metallurgy, 108, pp Magda, R Aspects of optimum mine site selection, Mining Science and Technology, 2, pp Narrei, S. & Osanloo, M Post mining land use methods optimum ranking, using multi attribute decision techniques with regard to sustainable resources management, OIDA International Journal of Sustainable Development, 11, pp Osanloo, M. & Ataei, M Factors affecting the selection of site for arrangement of pit rock dumps. Journal of Mining Science. 39, 2, pp Robertson, A.M Site selection and design for uranium mine waste and plant tailings. Proceedings of the 12th CMMI Congress, H.W. Glen (editor), Johannesburg: The South African Institute of Mining and Metallurgy, pp Saaty, T.L. & Vargas, L.G Decision making in economic, political, social, and technological environments with the Analytic Hierarchy Process, Pittsburgh: RWS Publications. Saaty, T.L Decision Making with Dependence and Feedback: The Analytic Network Process, Pittsburgh: RWS Publications. Samimi Namin, F., Shahriar, K., Bascetin, A. & Ghodsypour S.H FMMSIC: a hybrid fuzzy based decision support system for MMS (in order to estimate interrelationships between criteria), Journal of the Operational Research Society, 63, pp Shahriar, K A new approach to waste dump site selection according to fuzzy decision making process, Canadian institute of mining, metallurgy & petroleum (CIM Bulletin), 100, pp Shannon, C.E. & Weaver, W The mathematical theory of communication, Urbana: University of Illinois Press. Stevenson, W.J Production/operations management, 4th ed. Richard D. Irwin Inc., Homewood, 916 p. Tchobanoglous, G., Theisen, H. & Vigil, S.A Integrated solid waste management: engineering principles and management issues, McGraw Hill, New York, 211 p. Yavuz, M Selection of plant location in the natural stone industry using the fuzzy multiple 1782
71 23 rd attribute decision making method, The Journal of the Southern African Institute of Mining and Metallurgy, 108, pp Yazdani Chamzini, A Waste dump site selection by using fuzzy VIKOR, SME Annual Meeting, Seattle, WA, pp Zadeh, L.A Fuzzy sets, Information and Control 8, pp Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoningi, Info Sci. 8, pp
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81 23 rd Geostatistical Assessment of Collapses in Gole Gohar Open Pit Mine, Kerman, South West of Iran M.Shademan, H.Hassani, P.Moarefvand, H.Madani Amirkabir University of Technology, Tehran, Iran S.Karimi Nasab Gole Gohar Iron Ore Co, Kerman, Iran Shahid Bahonar University of Kerman, Kerman, Iran ABSTRACT Almost all collapses of rock slops especially in mines are related to discontinuities which include beddings, faults and major joints. Spatial distribution of collapses in open pit mines is related to distribution of discontinuities. Geostatistical assessments can be used for understanding the distribution of regionalized variables in any spatial study. In this paper, regionalized variable theory is used for analyzing and interpreting the spatial distribution of collapses taken place at Gole Gohar iron mine, which is located south west of Kerman city, Kerman province, and south west of Iran. In order to define regionalized variable distribution, at first step, variogram functions are determined for identifying the regional behavior. Furthermore, it is possible to estimate the tonnage of collapse for every local block on pit wall and prepare maps for the interpretation of behavior of the regionalized variable. Analysis of variograms showed that the tonnage of collapses have a spatial structure that make it possible to set up a geostatistical model to make a prediction of collapses for each block on the pit wall. Keywords: geostatistical assessment, regionalized variable, collapse, Gole Gohar open pit mine 1 INTRODUCTION Rock slope instabilities are a major hazard for human activities often causing economic losses, property damages and maintenance costs, as well as injuries or fatalities. Stability analyses are routinely performed in order to assess the safe and functional design of an excavated slope (e.g. open pit mining, road cuts, etc.), and/or the equilibrium conditions of a natural slope. The analysis technique chosen depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying strengths, weaknesses and limitations inherent in each methodology. It is less than 25 years since most rock slope stability calculations were performed either graphically or using a handheld calculator. The engineer today is presented with a vast range of methods for the stability analysis of rock and mixed rocksoil slopes; these range from simple infinite slope and planar failure limit equilibrium techniques to sophisticated coupled finite/distinct element codes. Geotechnical engineering is constantly evolving and its practitioners are always looking out for tools, which can improve design and help better handle the large 1793
82 M. Shademan, H. Hassani, P. Moarefvand. H. Madani, S. Karimi Nasab uncertainties and variations inherent in soil and rock properties. In recent years, several authors have attempted to apply geostatistics to the problems of geotechnical engineering. Geostatistics, as a methodology for estimating recoverable reserves in mining deposits, was mathematically formalized by French professor Georges Matheron 1963, inspired by the pioneering work of South African mining engineer D.G. Krig in the 1950's. Today it is extensively used in the mining and petroleum industries, and in recent years has been successfully integrated into remote sensing (Atkinson&Lewis, 2000, Qingmin Meng et al.,2009, PardoIguzquiza et al., 2011) and Geographic Information Systems (GIS) (Choi&Park,2006), soil scientists (Choi&Park,2006, Emery, 2006, Tavares, et al., 2008), hydrologists (Hossain, et al., 2007, Chowdhury,2010) as well as statisticians, so there are successful applications to a variety of fields. Geostatistical assessments can be used for understanding the distribution of regionalized variables in any spatial study. In this paper, regionalized variable theory is used for analyzing and interpreting the spatial distribution of collapses taken place at Gole Gohar iron mine which make it possible to predict collapses for each block on the pit wall. 2 GEOLOGICAL SETTING The Gole Gohar iron mine is located in the NW of SanandajSirjan adjacent to Zagros zone in Iran. The mining area is in 53 kilometers of South West of the Sirjan in latitudes to and longitudes of 29 3 to Given the tectonic setting, the remote sensing survey of the area around the mine, the geological survey of the mine and the area around the Gole Gohar mine, following results about structural geology model of mine were obtained. In the study area variety of faults consist of reverse, strike slip, normal faults and tensile major joints with considerable aperture are visible. Figure 1 shows distribution of faults around the pit No.1 of Gole Gohar mine. Figure 1. Distribution of faults around pit No.1 of Gole Gohar iron mine What is causing the above faults is existence of a subsurface right lateral strike slip fault with NWSE trend, which has to bend to the left. This situation has led a compressional lens shaped that its northeast and southwest boundary are thrust faults with dips towards the southwest and northeast, respectively. Structural geology section perpendicular to the strike of the zone is like a flower. 1794
83 23 rd Flower structure as a certain structure of deformation strike slip areas can be seen in pit No.1 (Fig. 2). In bedrock including ore body, faults often has eastwest trend with dip 45 to 80 degree toward the south. These faults almost are boundary between ore body and host rocks. Since these faults have small angle with the northern benches of mine and their slope is consistent with trenches slope, instability is inevitable(hasanpoor,2010). Figure 2. Flower faults structure in southwest wall of the Gole Gohar mine (Hasanpoor,2010). 3 DETERMINATION OF POTENTIAL FAILURE GEOMETRY To determine which failure modes are possible at a particular operation the geologic parameters in various sectors of the mine need to be quantified. Collecting information such as orientation, spacing, trace length, and shear strength with respect to major structures and other geologic features is an important key to determining failure potential. The basic failure modes which may occur are planar, wedge, circular and toppling failure (Osanloo, 2005, Girard, 2001). The types of failures occurred in pit No.1 of Gole Gohar mine which obtained in field survey is shown Figure 3. As shown in Figure 3, rock mass in Gole Gohar mine have potential of different kinds of failures. 4 METHODOLOGY The basic geostatistical tool for characterizing spatial variability is the variogram. is defined as half the average quadratic difference for N pairs of measurements of the variable z separated by a distance h (Armstrong, 1998, Isaaks&Srivastava, 1989, Journel, 1989, Journel&Huijbregts, 1978): (1) After calculation the experimental variogram, it is necessary to adjust the mathematical model to represent the variable as realistically as possible. It is important that the mathematical model represents the trend of the variogram with relation to distance h. Estimates obtained from kriging will then be more precise and reliable. 1795
84 M. Shademan, H. Hassani, P. Moarefvand. H. Madani, S. Karimi Nasab Figure 3. Types of failures occurred on the pit wall of Gole Gohar iron mine. (a) wedge failure, (b) planar failure, (c) toppling failure and (d) circular failure(hasanpoor,2010). Among the spatial interpolation (geostatistical estimation) techniques, a process called kriging is the best linear unbiased estimator (BLUE) of unknown characteristics (Isaaks&Srivastava, 1989, Journel, 1989), which make it possible to understand the regional behavior of the natural phenomena for every point in the study area (Krige, 1962). If magnitudes of data are available at specific locations, it is possible to estimate the values of it at other locations through Kriging. The goal of Kriging is to predict the average value of at specific point of study area. If are known values of parameter, then the estimated value of parameter at point x 0 is given by: (2) Where are weights applied to the respective values, such that: (3) The weights w i are determined through kriging matrix (Isaaks&Srivastava, 1989, Subyani, 1997). 5 GEOSTATISTICAL MODELING AND DISTRIBUTION OF TONNAGE OF COLLAPSE In this research the variable is the tonnage of collapses. Spatial distribution of collapses on the pit wall of Gole Gohar iron mine is shown in Figure
85 23 rd Figure 4. Spatial distribution of collapses on the pit wall of Gole Gohar iron mine. Here, the methodology is applied in order to represent the distribution of tonnage of collapse as regional variable. Investigation of the distribution of interest regionalized variable in the given pit wall is carried out by determining the variogram function. These functions are determined for identifying the regional behavior. Through experimental variograms calculated with all collapses data in several directions, the omnidirectional variogram which shows the best structure was chosen. The experimental variogram for collapse data was fitted using the spherical model which is presented in Figure 5. The optimum sill and range were chosen for variogram by cross validation method. The parameters of the variogram function are given in Table 1. After determining a theoretical variogram and running kriging technique using above mentioned methodology, it is possible to estimate the tonnage of possible collapses for every local block on pit wall and prepare maps for the interpretation of behavior of the regionalized variable. The kriging map of estimated blocks with the size of 25*25*10m in level 1594m is shown in Figure 6. Table 1. The parameters of the variogram function Variogram model Nugget (% 2 ) Sill (% 2 ) Range (m) Spherical
86 M. Shademan, H. Hassani, P. Moarefvand. H. Madani, S. Karimi Nasab Figure 5. Spherical model fitted to experimental variogram calculated for tonnage of possible collapses occurred in Gole Gohar iron mine. Figure 6. Tonnage Kriging map of possible collapse in level 1594m Comparing figures 1 and 6 shows, there is a relation between tonnage of possible collapses and existence of discontinuities specially faults around the pit area. In an another word, distribution of possible collapses in pit No.1 of Gole Gohar iron mine is related to distribution of discontinuities so covariance between tonnage of possible collapses and discontinuities in area could be an approach to evaluate safety factor. As shown in Figure 6, eastern and western walls are stable but there is possibility of collapse in northern and southern walls. Therefore, for development of exploitation in north and south walls of pit mine, some particular improvement methods such as unloading and maintenance system could be considered. 6 CONCLUSION In this paper, geostatistical analysis provides a three dimensional visualization of spatial variability of tonnage of collapse in open pit Gole Gohar iron mine. The first step of the application is to determine variogram 1798
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